OPS算法优化效果影响因素分析

OPS算法中目标函数以及如何获取目标函数最优解是决定算法优劣的重要因素。对比分析了4种目标函数和10种求最优解方法在网格数、初始点位置、迭代次数以及需求精度等因素变化时对OPS算法优化效果的影响。结果表明,在顶点移动过程中目标函数f1和f4变化较为光滑。采用不同目标函数时,随着网格数的增加优化时间随之增加,但优化后最差单元质量并无此规律;随着需求精度的增加,网格中最差单元质量和优化时间都有所增加,迭代次数变化对于优化时间和优化效果的影响可以忽略不计。采用变尺度法求解目标函数下降方向以及二次插值法进行一维搜索的第6种方法,在耗费时间、优化效果以及收敛速度等方面都显示出了较好的优势。

Analysis on factors influencing optimization of OPS algorithm

The objective function and how to obtain its corresponding optimal solution are key factors that determine the optimization-based smoothing algorithm to be good or on the contrary.The factors that affect optimizing effect,such as objective function and method of solving optimal solution under the change of element number,initial point position,interaction number and desired accuracy,were compared.It is found that the objective functions (f₁,f₄) are smooth when the position of node is changed.With the increase of element number,the time during optimization increases for the four objective functions,while the worst element quality varies only slightly.And with the increment of the desired accuracy,the mesh quality and the time consumed increase.The iteration number has little effect on the mesh quality and time cost for different functions.The sixth method combined with variable metric method to solve descent direction of objective function and quadratic interpolation as one-dimensional searching method shows better advantage over time,optimizing effect,and convergence speed.